Schrödinger-Maschine - New paths to physics-based neural networks

Machine learning is a driving force behind the recent societal upheavals caused by technological breakthroughs and an accompanying wave of automation and digitization. From face recognition to exploration of new materials and pharmaceuticals, recommendations, even autonomously driving cars are promised. These ideas have meanwhile also found their way into theoretical and applied physics, in the hope of new approaches to old unsolved problems. In the course of this, a disruptive, new research field has opened up with the aim of converting the successes from computer science to problems in physics and classic engineering. Since a pioneering work by Raissi, Perdikaris & Karniadakis in 2018/19 [see list of references below] on physically-informed neural networks, there have been unprecedented tectonic shifts in computational physics, scientific computing and simulation sciences in general. A learning machine, in this case an artificial neural network in particular, is provided with information about physical laws in the form of error signals from the outside during the learning process. This approach is simple and powerful, but inherently suffers from any problems that are already known from computer science, such as that these machines can only be successfully trained with very large amounts of data. These problems are mainly due to the fact that the physical knowledge is only offered as additional information - i.e. it is also learned, but is not directly and firmly anchored in the learning machine. However, the reality of the natural scientist looks completely different: In most cases, only little data is available, measured against the complexity of the learning machine and the associated amounts of data required. The typical scenario in the natural sciences therefore revolves around "smart data" and not "big data". In this project, a radically new approach is to be pursued, with which physical laws can be integrated directly into the inner structure of learning machines. The approach originates from a new perspective on physics-based machine learning through the lens of probability theory and so-called stochastic processes. A machine constructed on the basis of physical laws differs significantly in its complexity from machines that are only physically informed from the outside, and promises precision and computing speeds that exceed the state of research by a multiple. The contrast between physically-informed and physically-constructed is comparable to weak constraints vs. strong constraints in optimization (i.e. physical laws are approximately vs. exactly satisfied). The new concept is to be demonstrated using the basic equation of quantum mechanics; the Schrödinger equation. The aim of this project is to realize and demonstrate the so-called Schrödinger machine. Building on this, a new field of research could be established in Styria, for example with EU funding.